Energies 2010, 3, 1943-1959; doi:10.3390/en3121943 OPEN ACCESS
energies ISSN 1996-1073 www.mdpi.com/journal/energies Article
LES of a Meso Combustion Chamber with a Detailed Chemistry Model: Comparison between the Flamelet and EDC Models Angelo Minotti * and Enrico Sciubba Department of Mechanical & Aerospace Engineering, Sapienza University of Roma, via Eudossiana 18, 00184 Roma, Italy; E-Mail:
[email protected] * Author to whom correspondence should be addressed; E-Mail:
[email protected]; Tel.: +39-06-44-585-272. Received: 20 October 2010; in revised form: 17 November 2010 / Accepted: 8 December 2010 / Published: 10 December 2010
Abstract: The goal of this paper is to contribute to the design of high-performance mesocombustors, a field currently under rapid development, in particular for propulsion, e.g., for UAVs, and micro/meso-electrical power generators. This study is focused on a cylindrical combustor of 29 cm3, fuelled by methane and air, which provides 2 kW of thermal power. The device was entirely designed and built at the Sapienza University of Rome and coupled with an ultra-micro turbine. Two 3D LES simulations with detailed chemistry are presented. They differ only for the combustion models, so that a model comparison can be carried out. The calculated maximum temperature inside the chamber, the gas exhaust temperature and the combustion efficiency are compared and discussed. The results, reported at two different physical times, show the effects of the different combustion models, which predict different temperature and species concentration maps, but similar values for the combustion efficiency. Thermal, chemical and kinematic maps show that the Eddy Dissipation Concept allows for a more accurate estimatation of the performance parameters for application to first-order design procedures. Keywords: mesocombustion chamber; LES; Eddy Dissipation Concept; Flamelet model; detailed kinetics
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1. Introduction An investigation of the performance of a combustor for possible use in micro- and ultra-micro gas turbines for both stationary and propulsion applications is presented in this paper. The field of micro-meso thermo-electric/electronic devices is rapidly developing under the pressure of evermore stringent requirements posed by the increasing need for portable power generation. There are three main areas of interest for micro-meso-combustion: terrestrial and marine propulsion, UAV (“Unmanned Aerial Vehicles”) for tactical and meteorological recognissance, and portable electrical power generation. In the current literature [1,2] a mesoscale combustion regime is defined as one in which the flame scale is of the same order of magnitude as the thickness of the flame preheating zone. This implies that one of the characteristic dimensions of the combustor is of the order of the quenching diameter (millimeters to centimeters): According to this definition, the device studied here belongs to the class of meso-combustion chambers. Meso-scale systems behave differently than macro-scale ones, since in the former both the Reynolds and Peclet numbers are low, and consequently viscous and diffusive effects become more important. Low Reynolds implies low turbulent intensities or even laminar flow fields, so that the turbulent contribution to mixing processes is scarce or totally absent. At the same time, purely diffusive processes are too slow to be effective. Therefore, in scaled-down conventional combustors the conversion of chemical- into thermal energy can be severely limited by the decreased residence time, and in the worst case it can be totally prevented. The size reduction implies also larger heat losses that bring about a decline in the overall combustion efficiency and a reduction of the reaction temperatures, which in turn narrows the stability limits of the combustor by increasing the kinetic reaction times. For the above reasons, a proper management and understanding of the thermo chemical issues connected to size reduction are mandatory in order to build operationally efficient meso-combustors. Previous work in micro/meso-propulsion related to scaling laws issues [3–6] and focuses predominantly on fluid dynamics and combustion [7–18]. Three dimensional numerical simulations of methane-air combustion in swirling micro/meso-combustors are not common: the majority of the references available in the literature investigate the combustion process of propane in micro/meso sized combustor by assuming 2-D axi-symmetrical geometry and reduced kinetic mechanism [7–13,16–18]. Six of the above references deal with methane fuel, and while five of them [10,11,14–18] consider 2-D combustion chambers, only one of them analyzes 3-D swirling combustion chambers as in the present work; in [19] flame stabilization and flow evolution are analyzed mostly by means of experiments on swirling combustion chambers fueled by hydrogen, methane and propane. Microchambers are much smaller than the one presented here. Combustion efficiencies in excess of 90%, in particular with hydrogen, were reported; in combustion chambers smaller than 124 mm3, stable methane combustion could be achieved only by enriching air with oxygen. Results were compared with CFD simulations employing the global 1-step Westbrook and Dryer kinetic scheme [20]. Our work differs from that of [19] in two aspects: the chamber dimension and the accuracy of the chemical model.
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In the following, two simulation campaigns on the same combustion chamber are reported. In the “Flamelet simulation”, combustion is modeled by means of 67 “flamelets” pre-calculated and stored in look-up tables [21–28] using detailed chemistry [29] (GRIMech3.0, 53 species and 325 reactions, using Arrhenius relations). The “EDC simulation” employs the Eddy Dissipation Concept [30,31], and models chemistry with a detailed mechanism (GRIMech1.2) defined by 35 species and 177 reactions, using Arrhenius relations [32]. The EDC solves the species- and NS equations simultaneously. The GRIMech1.2 mechanism has been chosen to reproduce the chemistry as accurately as possible while abiding by the constraints posed by the CFD software (FLUENT6.3) [33] capabilities that limit the species equations to a maximum of 50. Both simulations are performed by means of a 3D unsteady LES method with the “WALE” (Wall Adapting Local Eddy Viscosity) subgrid scale model [34], following the results provided in [35]. Temperature, species maps and combustion efficiency values are the most important results presented and discussed. The “Flamelet simulation” results are provided after 0.03 s of physical time while those of the “EDC simulation” are provided at two different times, namely after 0.03 s (3 residence times) and 0.05 s (five residence times). The “EDC simulation” provides more realistic results than the first one, and it will be argued in the following that the differences result from the different assumptions posited by the two combustion models. This paper is structured as follows: Section 2 describes the domain geometry and the specified operating conditions; Section 3 contains a brief discussion of the turbulence models; Section 4 discusses the combustion and chemistry models; Section 5 reports the numerical models while Section 6 presents and discusses the results. This work is part of a broader work that includes an experimental analysis carried out at the Sapienza University of Roma, which will be reported and compared in a follow-up paper for a deeper understanding of combustion phenomena in microcombustion chambers. 2. Combustion Chamber and Operating Conditions The combustion chamber geometry is reported in Figure 1 (divided into slices for ease of visualization): The domain is discretized by 870,000 unstructured cells, so that y+ ≈ 5 and Δy+ ≈ 1; that is, the first point away from the wall is inside the viscous sublayer, where the velocity profiles, in spite of the high stretching imposed by the elongated geometry, are still parabolic. The diameter of the chamber is 0.025 m, its height 0.06 m (aspect ratio = 0.416), for a total volume of 29 cm3. The methane feeding duct has a diameter of 0.0015 m, the air duct 0.005 m. The exhaust duct on the lower side of the chamber has a diameter of 0.01 m. To improve mixing the gaseous methane is injected in the radial direction at 90° with respect to the air flow which is tangential to the chamber. The dimensions of the chamber have a strong influence on the mixing dynamics, and consequently on the combustion efficiency, due to the strong effects of the aspect ratio (S/V) on the mean streamline curvature and on the swirling motions.
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Operating and boundary conditions are reported in Table 1; mass flows at inlets are imposed, together with the pressure of 2 atm at the outlet section, while the walls are at constant temperature: Two different values were specified depending on the device zones: the chamber and air duct walls are at 700 K while the methane and exhaust ducts are at 300 K. The fuel inlet Reynolds number is in the transitional regime (ReCH4 = 1,500), while the Reair is fully turbulent (ReAIR = 14,700); this feature is characteristic (and peculiar) of microcombustors; it is well known that the possibility of relaminarization is enhanced by combustion that causes an increase of the effective viscosity of the burning mixture; on the other hand, the slight expansion inside of the chamber introduces a contrasting effect, so that the final regime is determined by the dynamic competition between these two effects. Figure 1. Representative geometry of the micro-combustion chamber.
Table 1. Operating Conditions. Parameter Mass Flow Rate (kg/s) Inlet Temperature (K) Outlet Pressure (atm) Inlet Velocity (m/s) Inlet Viscosity (kg/m-s) Re Chamber Wall Temperature (K) Methane Duct Wall Temperature (K) Air Duct Wall Temperature (K) Exhaust Duct Wall Temperature (K) Kinetic Energy Ratio, M Global equivalence ratio
Methane 3.93 × 10−5 300 2 18 2 × 10−5 1,500
Air 1.9 × 10−3 700 2 100 3.29 × 10−5 14,700 700 300 700 300 0.038 0.355
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The species isobaric specific heats are described by polynomials in T as per the GRIMech Thermo Data file [36] that has been included in the CFD code, while kinetic theory [37] is assumed to predict transport properties. 3. Turbulence and Combustion Models The LES modeling approach is applied in both simulations. They adopt the WALE (Wall Adapting Local Eddy viscosity) model [34] which is designed to return the correct y3 wall asymptotic behavior for wall bounded flows. As previously stated, the “flamelet simulation” uses the “non-adiabatic flamelet model” and the second the EDC model. The flamelet model, used in the non-premixed combustion model to account for chemical non-equilibrium, regards the turbulent flame as an ensemble of thin, laminar, locally one-dimensional flamelet structures embedded within the turbulent flow field [21,22,24–26]. Here 67 flamelets, with χ0 = 1 and Δχ = 2, have been used to describe combustion, where 2D f 2 is the scalar dissipation [s−1], D is the diffusion coefficient and f is the mixture fraction. N equations are solved for the species mass fractions, Yi: Yi 1 2Yi 2 Si t 2 f
(1)
while the energy equation is solved for the temperature:
T 1 2T 1 2 t 2 f cp
1
H S 2c i
i
c p Y T c pi f f i f
i
p
(2)
Equations 1 and 2 are solved separately and previously than the NS equations and stored in look-up tables as function of f and χ only. This means that the initialization field is the one at equilibrium in every cell, hence reaction rates do not respect the real thermodynamic conditions inside the chamber. Reactions are described by the GRIMech3.0 [29] chemical mechanism (53 species and 325 reactions). The “EDC simulation” adopts the Eddy Dissipation Concept [31]. It assumes that reactions occur in small turbulent structures, called the fine structures [30], under a steady state assumption, according to the law: Ri
*
2
* 1 *
3
Y
i
*
Yi
(3)
1
2 where Yi is the fine-scale species mass fraction after reacting over the time * C . Chemistry is defined by the GRIMech1.2 [32] chemical mechanism (35 species and 177 reactions). Even though the two chemistry models differ both for the number of species they consider and for the number of reactions they include in the calculations, the results presented in this work can be under the specified assumptions- directly compared, for the following reasons: *
(a) The flamelet model is an equilibrium model, and as such it provides the solution at a hypothetical (locally steady) equilibrium: ignition delay is explicitly neglected, and therefore the only global quantity of interest is the final combustion temperature;
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(b) GRIMech1.2 and GRIMech3 predict in fact slightly different ignition delays, but this is unessential in this study, in which the comparison is made at the final equilibrium conditions. To witness, Table 2 reports the difference in the adiabatic flame temperature for several equivalence ratios and ignition temperatures: it is apparent that, in the range of interest here (see the temperature maps in Figures 8–10), the deviations are less than 0.5%. Table 2. Final Temperature % difference between GRIMech3.0 and GRIMech1.2. Reactants
Φ = 0.3
Φ = 0.5
Φ = 0.7
Φ = 1.1
Φ = 1.3
Φ = 1.5
1000
0.00%
−0.6%
–0.6%
–0.4%
1100
0.00%
–0.7%
–0.6%
–0.5%
–1.4%
–0.4%
–0.3%
4.2%
–0.04%
0.00%
–0.4%
–1.3%
–0.5%
–0.3%
3.5%
–0.04%
0.00%
–0.5%
1200
0.00%
–0.7%
–0.6%
–0.5%
–1.3%
–0.5%
–0.4%
2.8%
–0.04%
–0.04%
–0.5%
1300
–0.1%
–0.8%
–0.6%
–0.5%
–1.2%
–0.5%
–0.4%
–0.2%
–0.1%
–0.04%
–0.5%
1400
–0.1%
–0.9%
1500
–0.1%
–0.8%
–0.6%
–0.5%
–1.2%
–0.5%
–0.4%
–0.3%
–0.1%
–0.04%
–0.5%
–0.6%
–0.5%
–1.1%
–0.5%
–0.4%
–0.3%
–0.2%
–0.04%
–0.5%
1600
–0.1%
–0.8%
–0.5%
–0.5%
–1.1%
–0.5%
–0.4%
–0.3%
–0.1%
–0.1%
–0.5%
1700
–0.1%
–0.7%
–0.5%
–0.5%
–1.0%
–0.5%
–0.4%
–0.3%
–0.1%
–0.1%
–0.5%
1800
–0.3%
–0.7%
–0.5%
–0.5%
–1%
–0.5%
–0.5%
–0.3%
–0.2%
–0.1%
–0.5%
1900
–0.2%
–0.6%
–0.4%
–0.5%
–0.9%
–0.5%
–0.5%
–0.3%
–0.2%
–0.1%
–0.5%
2000
–0.2%
–0.5%
–0.6%
–0.5%
–0.9%
–0.5%
–0.5%
–0.4%
–0.3%
–0.1%
–0.5%
Temperature (K)
Φ = 0.9
Φ=1
Φ = 1.7
Φ = 1.9
Φ = 1.1
4. Numerical Models Simulations have been carried out with a Pressure-Based solver which employs an algorithm of the general class of “projection methods” [38]. In this method the constraint of mass conservation (continuity) of the velocity field is imposed by solving a pressure correction equation. This solver (Fluent 6.3) uses a solution algorithm where the governing equations are solved sequentially (segregated from one another). The SIMPLEC (SIMPLE-Consistent algorithm) [39], with a skewness correction (particularly useful with this high curvature geometry) is used to resolve the pressure-velocity correcting equation; the SIMPLEC uses a relationship between velocity and pressure corrections to enforce mass conservation and to obtain the pressure field. The unsteady formulation is discretized by a central 2nd order implicit scheme. The momentum equation, the energy and mixture fraction equations are discretized by the 3rd order MUSCL (Monotone Upstream-Centered Schemes for Conservatives Laws) scheme [40]: This scheme is derived by blending a central differencing scheme and a 2nd order upwind scheme. The pressure equation is discretized by a 2nd order method. 5. Results and Discussion In the following a comparison between the two simulations is provided. For the sake of clarity all figures show the flowfields on slices located at 0.01 m, 0.03 m and 0.055 m, (the first and last being the inlet- and outlet plane respectively) and they are provided, wherever possible, using the same scale.
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The results shown here correspond to two different physical times, namely 0.03 s and 0.05 s (three and five residence times, respectively). The mean residence time can be defined as the time a parcel of gas spends inside the combustor, its value estimated as the ratio between the mass of gas in the chamber volume, Vc , and the mass flow rate, m :
residence
Vc 0.01 s m
(4)
The total mass flow rate was computed from the data in Table 1, while the averaged gas density, , is assumed equal to that of air at 1,100 K and 2 bar (0.62 kg/m3). Assuming this residence time as the characteristic combustion chamber fluid dynamics time, and comparing it with data in Tables 3 and 4, it is possible to deduce a “worst case Damkoehler number”. The Damkoehler number, Da, defines the fluid-dynamics/chemical times ratio and indicates whether the reactions are completed within a given time (Da >> 1), or are frozen (Da > 1 (complete reactions), combustion temperatures must be ≥1,300 K with Φ ~ 0.9. Figure 6 shows that wide zones of the chamber are well above 2,000 K. The iterative solution was assumed converged when the difference between inlet and outlet mass flowrate, ∆m/∆t, was
